Question

A block of mass $150$ g moves with a uniform speed in a circular groove of radius $30$ cm. Find its centripetal acceleration and the centripetal force acting on the block if linear speed of the block is ${8ms}^{-1}$

• A. $3.2217$ N
• B. $22.51$ N
• C. $3.1451$ N
• D. $32$ N

Answer 1

The correct option is D $32$ N

Mass of block, $m=150$ $g=150\times {10}^{-3}$ $kg$

Radius, $r=30$ $cm=30\times {10}^{-2}$ $m$

Linear velocity, $v=8$ $m/s$

Centripetal acceleration, $a=\frac{v^2}{r}$

$\Rightarrow a=\frac{64}{30\times {10}^{-2}}$

$\Rightarrow a=\frac{32}{15}\times {10}^2$ $m/s^2$

$\Rightarrow a=213.33$ $m/s^2$

Centripetal force, $F=ma$

$\Rightarrow F=150\times {10}^{-3}\times \frac{32}{15}\times {10}^2$

$\Rightarrow F=32$ $N$